Some (though not all) previous studies have documented the interlanguage speech intelligibility benefit (ISIB), i.e. the greater intelligibility of non-native (relative to native) speech to non-native listeners as compared to native listeners. Moreover, some studies (again not all) found that native listeners consider foreign-accented statements as less truthful than native-sounding ones. We join these two lines of research, asking whether foreign-accented statements sound more credible to non-native than to native listeners and whether difficult-to-process (less comprehensible) utterances are less credible. In two experiments we measure the intelligibility, comprehensibility and credibility of native and foreign-accented statements for native listeners and non-native listeners matched or mismatched in L1 with non-native talkers. We find an ISIB in both matched and mismatched non-native listeners, and an analogous matched comprehensibility benefit. However, we obtain no evidence of an interlanguage speech credibility benefit. Instead, both matched and mismatched non-native listeners tend to trust native statements more (i.e. statements produced by their target-language models). For native listeners, we do not confirm the tendency to mistrust non-native statements, but we do find a moderate correlation between the comprehensibility and credibility of foreign-accented utterances, giving limited support to the hypothesis that decreased perceptual fluency leads to decreased credibility.